Is it possible to have the latent vector of an auto-encoder with size 1?
According to various experimentation on autoencoders, it is very possible to have latent vector of size 1. Various layers can help the downsizing of the original input to a very small size of 1. But an issue may arise during decoding. If you're expecting that through one or two or maybe five layers in decoder you can achieve an accurate reconstruction, it is highly unlikely abd the result will turn out to be blurry. Maybe a great network with various parameters may help the reconstruction without considering generalization as asked by you.